Optimal. Leaf size=21 \[ \frac {11}{2} \left (1+2 x-\left (-4+x+e^2 x\right )^2\right ) \]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 28, normalized size of antiderivative = 1.33, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {6} \begin {gather*} -\frac {11}{2} \left (1+e^4\right ) x^2-11 e^2 (2-x)^2+55 x \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 6
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (55+e^2 (44-22 x)+\left (-11-11 e^4\right ) x\right ) \, dx\\ &=-11 e^2 (2-x)^2+55 x-\frac {11}{2} \left (1+e^4\right ) x^2\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 36, normalized size = 1.71 \begin {gather*} -11 \left (-5 x-4 e^2 x+\frac {x^2}{2}+e^2 x^2+\frac {e^4 x^2}{2}\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.52, size = 27, normalized size = 1.29 \begin {gather*} -\frac {11}{2} \, x^{2} e^{4} - \frac {11}{2} \, x^{2} - 11 \, {\left (x^{2} - 4 \, x\right )} e^{2} + 55 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.12, size = 27, normalized size = 1.29 \begin {gather*} -\frac {11}{2} \, x^{2} e^{4} - \frac {11}{2} \, x^{2} - 11 \, {\left (x^{2} - 4 \, x\right )} e^{2} + 55 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.02, size = 26, normalized size = 1.24
method | result | size |
gosper | \(-\frac {11 x \left (x \,{\mathrm e}^{4}+2 \,{\mathrm e}^{2} x -8 \,{\mathrm e}^{2}+x -10\right )}{2}\) | \(26\) |
risch | \(-\frac {11 x^{2} {\mathrm e}^{4}}{2}-11 x^{2} {\mathrm e}^{2}+44 \,{\mathrm e}^{2} x -\frac {11 x^{2}}{2}+55 x\) | \(29\) |
norman | \(\left (44 \,{\mathrm e}^{2}+55\right ) x +\left (-\frac {11 \,{\mathrm e}^{4}}{2}-11 \,{\mathrm e}^{2}-\frac {11}{2}\right ) x^{2}\) | \(30\) |
default | \(-\frac {11 x^{2} {\mathrm e}^{4}}{2}+{\mathrm e}^{2} \left (-11 x^{2}+44 x \right )-\frac {11 x^{2}}{2}+55 x\) | \(33\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.38, size = 27, normalized size = 1.29 \begin {gather*} -\frac {11}{2} \, x^{2} e^{4} - \frac {11}{2} \, x^{2} - 11 \, {\left (x^{2} - 4 \, x\right )} e^{2} + 55 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.06, size = 24, normalized size = 1.14 \begin {gather*} x\,\left (44\,{\mathrm {e}}^2+55\right )-x^2\,\left (11\,{\mathrm {e}}^2+\frac {11\,{\mathrm {e}}^4}{2}+\frac {11}{2}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.06, size = 27, normalized size = 1.29 \begin {gather*} x^{2} \left (- \frac {11 e^{4}}{2} - 11 e^{2} - \frac {11}{2}\right ) + x \left (55 + 44 e^{2}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________